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This paper deals with the control of a prey species (as an unwanted species) in a predator-prey system. We consider a scenario where there are two control means available and they are applied in a state-dependent impulsive way, meaning that when the population of the harmful species is lower than a preset threshold, no control measure will be implemented; while when it reaches the threshold, the two control means will be used either in alternating order or random order. We formulate a general mathematical model for this scenario to evaluate the effect of such a control strategy by exploring the dynamics of this model. We define a one-dimensional map (Poincaré map) and by using the properties of this map, we derive sufficient conditions for the existence and global stability of an order-k periodic solution. By using the analogue of Poincaré criterion and bifurcation theory, we also establish sufficient conditions for a transcritical bifurcation near the predator-free periodic solution. Finally, we apply the results for the general model to two particular cases from two distinct fields: (I) integrated pest control and (II) tumour control with a comprehensive therapy. For (I), theoretical and numerical results show that the outbreak period of the pest is longer when two pesticides are applied randomly than when the alternating strategy is used. For (II), we find that the treatment frequency of drug rotation strategy is lower than that of no drug change strategy, and that the higher the control intensity, the lower the treatment frequency. [ABSTRACT FROM AUTHOR]

• A novel Filippov epidemic system involving three containment strategies is constructed. • Rich local and global sliding bifurcations indicate multi-stability dynamics. • Well data fitting results for epidemics A/H1N1 and COVID-19 reveal the applicability of the proposed model. • The final infected population can be maintained in a desired level through the proposed Filippov control measures. A non-smooth SIR Filippov system is proposed to investigate the impacts of three control strategies (media coverage, vaccination and treatment) on the spread of an infectious disease. We synthetically consider both the number of infected population and its changing rate as the switching condition to implement the curing measures. By using the properties of the Lambert W function, we convert the proposed switching condition to a threshold value related to the susceptible population. The classical epidemic model involving media coverage, linear functions describing injecting vaccine and treatment strategies is examined when the susceptible population exceeds the threshold value. In addition, we consider another SIR model accompanied with the vaccination and treatment strategies represented by saturation functions when the susceptible population is smaller than the threshold value. The dynamics of these two subsystems and the sliding domain are discussed in detail. Four types of local sliding bifurcation are investigated, including boundary focus, boundary node, boundary saddle and boundary saddle-node bifurcations. In the meantime, the global bifurcation involving the appearance of limit cycles is examined, including touching bifurcation, homoclinic bifurcation to the pseudo-saddle and crossing bifurcation. Furthermore, the influence of some key parameters related to the three treatment strategies is explored. We also validate our model by the epidemic data sets of A/H1N1 and COVID-19, which can be employed to reveal the effects of media report and existing strategy related to the control of emerging infectious diseases on the variations of confirmed cases. [ABSTRACT FROM AUTHOR]

• Periods of epidemics induced by different strains in Asian countries were classified by k-shape and hierarchical clustering methods. • Using correlation and regression analysis to explore the results of clustering Asian countries. • Revealing the reasons behind the development pattern of the epidemic in Asian countries. • Peak value of confirmed cases per capita in the Omicron phase are much higher, while mortality rate is significantly lower than in the earlier phases. • Vaccination rates were associated with lower mortality given the nature of the analysis. The COVID-19 epidemic has lasted for more than two years since the outbreak in late 2019. An urgent and challenging question is how to systematically evaluate epidemic developments in different countries, during different periods, and to determine which measures that could be implemented are key for successful epidemic prevention. In this study, SBD distance-based K-shape clustering and hierarchical clustering methods were used to analyse epidemics in Asian countries. For the hierarchical clustering, epidemic time series were divided into three periods (epidemics induced by the Original/Alpha, Delta and Omicron variants separately). Standard deviations, the Hurst index, mortality rates, peak value of confirmed cases per capita, average growth rates, and the control efficiency of each period were used to characterize the epidemics. In addition, the total numbers of cases in the different countries were analysed by correlation and regression in relation to 15 variables that could have impacts on COVID-19. Finally, some suggestions on prevention and control measures for each category of country are given. We found that the total numbers of cases per million of a population, total deaths per million and mortality rates were highly correlated with the proportion of people aged over 65 years, the prevalence of multiple diseases, and the national GDP. We also found significant associations between case numbers and vaccination rates, health expenditures, and stringency of control measures. Vaccinations have played a positive role in COVID-19, with a gradual decline in mortality rates in later periods, and are still playing protective roles against the Delta and Omicron strains. The stringency of control measures taken by a government is not an indicator of the appropriateness of a country's response to the outbreak, and a higher index does not necessarily mean more effective measures; a combination of factors such as national vaccination rates, the country's economic foundation and the availability of medical equipment is also needed. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics". [ABSTRACT FROM AUTHOR]

• A novel mathematical model is proposed to describe the heterogeneity of control interventions. • Xi'an presents a lower transmission probability but a higher reproduction number. • Enhancing closed-off management, tracing and testing intensities, are effective. • Citywide lockdown is not essential when the closed-off management is strictly implemented. • Enhancing tracing strategy is more effective than enhancing testing strategy in the early stage. Several local outbreaks have occurred and been suppressed with the dynamic zero-COVID policy and widely promoted vaccination program implemented in China. The epidemic duration and final size vary significantly in different cities, which may be attributed to different implementation patterns and intensities of non-pharmaceutical interventions (NPIs). It's important to capture the underlying mechanism to explore more efficient implementation patterns of NPIs in order to prevent the future resurgence. In this study, outbreaks caused by Delta variant in Xi'an, Yangzhou and Guangzhou in 2021 are chosen as the examples. A novel model dividing the population into three groups is proposed to describe the heterogeneity of control interventions. The model is calibrated and key parameters related to NPIs are estimated by using multi-source epidemic data. The estimation results show a lower transmission probability but a higher initial reproduction number in Xi'an. Sensitivity analysis are conducted to investigate the impact of various control measures in different epidemic phases. The results identify the vital role of enhancing closed-off management, strengthening tracing and testing intensities, on shortening the epidemic durations and reducing the final size. Further, we find that sufficiently implemented closed-off management would prevent the city from lockdown. Strengthening the tracing other than the testing strategy in the initial stage is more effective on containing the epidemic in a shorter duration with less infections. [ABSTRACT FROM AUTHOR]

• Countries pursuing 'zero COVID' rely on strong restrictions or even city lockdown. • Optimally balancing restrictions's length and confidence that the outbreak is ending is important. • The proportion of cases who miss the intervention restrictions and thus are capable of causing secondary transmission is estimated. • An iterative method is designed to quantify the daily end-of-outbreak confidence since the last reported case. • The projection of the end-of-outbreak day relies on the size of reproduction number and the acceptable risk threshold assuming the invariant distribution of serial interval. The end-of-outbreak declaration is an important part of epidemic control, marking the relaxation or cancellation of prevention and control measures. We propose a probability model to retrospectively quantify the confidence of giving the end-of-outbreak declaration during the COVID-19 epidemic in early 2020 in Wuhan. By using the linear spline, we firstly estimates the time-varying proportion of cases who miss the nonpharmaceutical interventions (NPIs) among all reported cases. Assuming the reproduction numbers being 1.5, 2.0, 3.0, 4.0, 5.0 and 6.0, the respective probability of the end of the COVID-19 outbreak with time after the last reported case can be iteratively computed. Consequently, the varying reproduction numbers produce slightly different increasing patterns of NPI effectiveness, and the end-of-outbreak declarations with 95% confidence are projected consistently earlier than the day when the lockdown was actually lifted. The reason for the timing discrepancy is discussed as well. [ABSTRACT FROM AUTHOR]